- A family has two children. Assume that birth month is independent of gender, with boys and girls equally likely and all months equally likely, and assume that the elder child’s characteristics are independent of the younger child’s characteristics. (b) Find the probability that both are girls, given that at least one is a girl who was born in March.
The solution gives like this: P (both girls|at least one March-born girl) =
P (both girls, at least one born in March)/P(at least one March-born girl)
=(1/4)(1-(11/12)^2)/(1-(23/24)^2)
I am really confused where the (23/24)^2 comes from? If considering opposite should be something like: No girl 1/4, one girl with birthday not in March 1/2*(11/12), and two girl with birthdays not in March(same as numbertor). can anyone help me figure out?
Thanks a lot.